![3. (12 pt) Suppose that S is the subset of R2 that contains all vectors on the two lines y = x and y = -2 s={[x] € R: y=x or](http://img.homeworklib.com/questions/2527b440-2306-11eb-ba66-8749a49b201d.png?x-oss-process=image/resize,w_560)
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![let s= {[!] em? : 4+7 (92-x} Solution @ @ s contains zero vector True because 0=0 = Coles: S is closed under scalar multiplic](http://img.homeworklib.com/questions/25ec7020-2306-11eb-b05d-2395c0217a2e.png?x-oss-process=image/resize,w_560)
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3. (12 pt) Suppose that S is the subset of R2 that contains all vectors on...
Problem 5. (1 point) Let H be the subset of vectors [x. y] in R2 such that the polint (x, y) les ...
Problem 5. (1 point) Let H be the subset of vectors [x. y] in R2 such that the polint (x, y) les between the lines y -3x and y x/3. (See the picture.) 1. Is H nonempty? choose 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and syntax such as [1.2]. 13,4] 3 Is H closed under...
1 point) Let V R2 and let H be the subset of V of all points...
1 point) Let V R2 and let H be the subset of V of all points on the line-4x-3y-0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? | H does not contain the zero vector of V | 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and...
Question 3 T Let S be the set of vectors in R2 which satisfy the property...
Question 3 T Let S be the set of vectors in R2 which satisfy the property ry > 0. Y Is S a subspace of R2? O Sis a subspace of R2 O Sis not a subspace of R2 because S does not contain the zero vector. S is not a subspace of R2 because S is not closed under vector addition. O Sis not a subspace of R2 because S is not closed under scalar multiplication.
Determine whether each statement is True or False. Justify each answer. a. A vector is any...
Determine whether each statement is True or False. Justify each answer. a. A vector is any element of a vector space. Is this statement true or false? O A. True by the definition of a vector space O B. False; not all vectors are elements of a vector space. O C. False; a vector space is any element of a vector. b. If u is a vector in a vector space V, then (-1) is the same as the negative...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x, y) |z 2 0,y S 0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H,...
Can you please answer questions 1-6，thank you a lot！Thumbs up for great answer，Thx！ Remember: to show...
Can
you please answer questions 1-6，thank you a lot！Thumbs up for great
answer，Thx！
Remember: to show that a property is true you must check every possibility (probably using variables and general vectors). To show that a property is false you only need to give one counterexample. 1. Find a set of vectors in R2 which is closed under vector addition but not scalar multiplication. 2. Find a set of vectors in R? which is closed under scalar multiplication but not...
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of...
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.
Find a proper subset of V1 which is a subspace of R4 and contains a vector of the form (∗, ∗, 3, 3).
These 2 qns mainly(ii) Find a proper subset of V1 which is a subspace of R4 and contains a vector of the form (∗, ∗, 3, 3). (iv) Is it possible to find a subset of V2 which satisfies the closure properties under vector addition and scalar multiplication? Justify your answer.
Problem 6. Suppose Vj = 0 , 02 = 0 02) = 0 Consider the subset...
Problem 6. Suppose Vj = 0 , 02 = 0 02) = 0 Consider the subset W of R$ consisting of all vectors w for which w.vi) ( w (a) Show that W is closed under scalar multiplication, (b) Show that W is not a subspace of R.
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a...
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. () The set w = {(0,x2,x): and X" are real numbers) is a subspace of R. False, this set is not closed under addition...
Problem 5. (1 point) Let H be the subset of vectors [x. y] in R2 such that the polint (x, y) les between the lines y -3x and y x/3. (See the picture.) 1. Is H nonempty? choose 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and syntax such as [1.2]. 13,4] 3 Is H closed under...
1 point) Let V R2 and let H be the subset of V of all points on the line-4x-3y-0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? | H does not contain the zero vector of V | 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and...
Question 3 T Let S be the set of vectors in R2 which satisfy the property ry > 0. Y Is S a subspace of R2? O Sis a subspace of R2 O Sis not a subspace of R2 because S does not contain the zero vector. S is not a subspace of R2 because S is not closed under vector addition. O Sis not a subspace of R2 because S is not closed under scalar multiplication.
Determine whether each statement is True or False. Justify each answer. a. A vector is any element of a vector space. Is this statement true or false? O A. True by the definition of a vector space O B. False; not all vectors are elements of a vector space. O C. False; a vector space is any element of a vector. b. If u is a vector in a vector space V, then (-1) is the same as the negative...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x, y) |z 2 0,y S 0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H,...
Can
you please answer questions 1-6，thank you a lot！Thumbs up for great
answer，Thx！
Remember: to show that a property is true you must check every possibility (probably using variables and general vectors). To show that a property is false you only need to give one counterexample. 1. Find a set of vectors in R2 which is closed under vector addition but not scalar multiplication. 2. Find a set of vectors in R? which is closed under scalar multiplication but not...
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.
Problem 6. Suppose Vj = 0 , 02 = 0 02) = 0 Consider the subset W of R$ consisting of all vectors w for which w.vi) ( w (a) Show that W is closed under scalar multiplication, (b) Show that W is not a subspace of R.
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. () The set w = {(0,x2,x): and X" are real numbers) is a subspace of R. False, this set is not closed under addition...
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